Question: Rewrite as a simplified fraction. ${2.3\overline{8} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 238.8888...\\ 10x &= 23.8888...\end{align*}}$ Subtracting the two equations, we have: ${90x = 215}$ ${x = \dfrac{215}{90}} $ ${x = \dfrac{43}{18}} \text{or} {2 \dfrac{7}{18}}$